President Obama's reported outreach to Iran to beseech the Islamic Republic to think about shared interests in fighting ISIS is raising eyebrows in Congress, where criticism of the administration is mounting over Obama's reluctance to bring a nuclear deal before lawmakers.

The Wall Street Journalreported that Obama secretly wrote to Supreme Leader Ayatollah Ali Khamenei last month, with the dual purpose of getting help on fighting ISIS and paving the way toward the Nov. 24 P5+1 nuclear-deal deadline.

Khamenei has declared that Iran will never give up its nuclear program.

The report emerged a few days before Secretary of State John Kerry is scheduled to meet with his counterpart, Foreign Minister Javad Zarif, in Oman.

White House press secretary Josh Earnest told reporters today that he's "not in a position to discuss private correspondence between the president and any world leader."

"I can tell you that the policy that the president and his administration have articulated about Iran remains unchanged. The United States is engaged in conversations with Iran in the context of the P5+1 talks to resolve the international community's concerns about Iran's nuclear program," Earnest said.

"And we have also discussed on the sidelines of those talks on at least a couple of occasions, the ongoing campaign that is being conducted against ISIL by the United States and 60 members of -- now more than 60 members who are part of this broader coalition," he continued.

"The United States will not cooperate militarily with Iran in that effort. We won't share intelligence with them. But their interests in the outcome is something that's been widely commented on -- commented upon and something that on a couple of occasions has been discussed on the sidelines of other conversations."

Still, when pressed, Earnest would not confirm or deny that the correspondence had taken place.

The spokesman said there wasn't a lack of transparency in sneaking a letter to the ayatollah because "the fact of the matter is there are also secret conversations between the administration and Congress about our negotiating strategy with Iran."

"I'm not saying that we're going to read them in after we cut a deal. I'm saying that we've been reading them in as we've been trying to negotiate this deal."

Regarding ISIS, Earnest stressed "it's not in the interest of Iran or, frankly, nobody else in this region of the world to have this extremist group rampaging across the countryside, carrying out terrible acts of violence."

"We do seek to -- or at least we have on a couple of occasions, sought to engage them on the sidelines of other talks to make sure that they understand what we're trying to do here, and to get a sense about their perspective on things."

State Department press secretary Jen Psaki was even more mum about the letter. "Anyone above the secretary, I assume you're referring to the president," she said. "So certainly, I'm not going to answer or address questions on that."

Psaki said they've "obviously" discussed ISIS on the sidelines of nuclear talks.

"But in terms of working with them, I don't think -- I wouldn't see it as a prerequisite" to a nuclear deal, she said. "We're not at the point of doing that, and there's no plans to coordinate with them militarily."

House Speaker John Boehner (R-Ohio) said there's reason to cast deep skepticism on both the letter and the nuclear deal.

"Listen, I don't trust the Iranians. I don't think that we need to bring them into this," Boehner told reporters today.

"And I would hope that the negotiations that are underway are serious negotiations. But I have my doubts."